\psset{unit=0.7,algebraic}
\begin{pspicture*}(-3,-3)(5.5,3)
\psaxes[labelFontSize=\scriptstyle,ticksize=-3pt 0,labelsep=2pt]{<->}(0,0)(-2,-3)(4,3)
\psplot[linecolor=blue]{0.0001}{4}{ln(x)}
\psplot[linecolor=blue]{0.0001}{4}{ln(x)/ln(10)}
\psplot[linecolor=blue]{0.0001}{4}{ln(x)/ln(0.5)}
\footnotesize
\rput[l](2,1.5){$f(x)=\ln x$}
\rput[l](3.5,0.3){$f(x)=\log_{10}x$}
\rput[l](0.3,2.7){$f(x)=\log_{1/2}x$}
\end{pspicture*}